Electromagnetic wave propagation in metamaterials: A visual guide to Fresnel-Kummer surfaces and their singular points

Favaro, Alberto

doi:10.1109/ursi-emts.2016.7571473

Cited by 4 publications

(7 citation statements)

References 26 publications

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“…The generalized Fresnel equation (117) spans the Fresnel surface. We present three typical cases for visualizing it, see also Favaro [40]. In Fig.…”

Section: Hadamard's Method Tamm-rubilar Tensor Densitymentioning

confidence: 98%

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On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

Hehl

Itin

Obukhov

2016

Int. J. Mod. Phys. D

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In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton's gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical * Based on an invited talk given at the Annual Meeting of the German Physical Society (DPG) in Berlin on 20 March 2015, "Working Group on Philosophy of Physics (AGPhil)". We sincerely thank Dennis Lehmkuhl (Wuppertal, now Pasadena) and his co-organizers Meinard Kuhlmann (Mainz) and Wolfgang Pietsch (Munich) [92] for the invitation. In the present version, we appreciably enriched our text by adding more formalism. We apologize to the philosophers for any inconvenience. A short version of this paper will be submitted to the International Journal of Modern Physics D.

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“…The generalized Fresnel equation (117) spans the Fresnel surface. We present three typical cases for visualizing it, see also Favaro [40]. In Fig.…”

Section: Hadamard's Method Tamm-rubilar Tensor Densitymentioning

confidence: 98%

“…Similarly to (40), we use the step-function representation for the electromagnetic excitation H and introduce the jump 2-form…”

Section: The Maxwell Equations In Premetric 3-vector Formmentioning

confidence: 99%

On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

Hehl

Itin

Obukhov

2016

Int. J. Mod. Phys. D

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“…where χ λνσκ is a constitutive tensor density of rank 4 and weight +1, with the dimension Let us consider the wave propagation in a local and linear medium described by means of the tensor density in (15). Then it turns out that in 3d space in the geometric optics approximation the waves span a (quartic) Kummer surface.…”

Section: Lagrange-hamilton Formalism: Action H As a New Physical Dime...mentioning

confidence: 99%

“…Then it turns out that in 3d space in the geometric optics approximation the waves span a (quartic) Kummer surface. These Kummer surfaces are determined by the quartic algebraic equation K λνσκ k λ k ν k σ k κ = 0, with the wave covector k µ and the Kummer tensor density K λνσκ (χ), which itself is defined as an expression cubic in terms of the constitutive tensor density χ λνσκ ; for details see Baekler et al [1] and for applications Favaro et al [14,15]. In vacuum, these Kummer surfaces degenerate to light spheres, see [35].…”

Section: Lagrange-hamilton Formalism: Action H As a New Physical Dime...mentioning

confidence: 99%

Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

Hehl

Lämmerzahl

2019

Annalen der Physik

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The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, it naturally leads one, besides the dimensions of length and time, to the fundamental units of action h, electric charge q, and magnetic flux φ. Also, q × φ = action and q/φ = 1/resistance are known. These results of classical physics suggests to look into the corresponding quantum aspects of q and φ (and also of h): The electric charge occurs exclusively in elementary charges e, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, φ appears quantized in the form of fluxons (Abrikosov vortices). And h leads, of course, to the Planck quantum h. Thus, one is directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity.

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“…In other words, the k-vectors of the plane waves that satisfy Maxwell's equations belong to a quartic surfaces ( ) in kspace (see example in Fig. 1(b)) [3,[11][12][13]. Each point on such a photonic quartic surface corresponds to a solution of Eq.…”

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confidence: 99%

Inverse problem of quartic photonics

Mulkey

Durach

2018

Opt. Lett.

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We formulate and solve the inverse problem of quartic photonics, or photonics of metamaterials, whose k-surfaces (also known as iso-frequency surfaces or Fresnel surfaces) are quartic surfaces. This provides an approach to engineer the effective parameters of metamaterials starting from the desired plane waves. We apply our method to the design of the high-k limit of metamaterials, extreme non-reciprocity, and complex bi-anisotropic media.

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Electromagnetic wave propagation in metamaterials: A visual guide to Fresnel-Kummer surfaces and their singular points

Cited by 4 publications

References 26 publications

On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

Inverse problem of quartic photonics

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